Orthogonal frequency division multiplexing (OFDM) is a well known communications technique that divides a communications channel into a number of equally spaced frequency bands. A subcarrier carrying a portion of the user information is transmitted in each band. Each subcarrier is orthogonal (i.e. independent of each other) with every other subcarrier, differentiating OFDM from commonly used frequency division multiplexing (FDM). OFDM (also known as multitone modulation) is presently used in a number of commercial wired and wireless applications. In wired applications, it is used in digital subscriber line (DSL) systems. In wireless applications, OFDM is used in television and broadcast radio such as the European digital broadcast television standard as well as in digital radio in North America. OFDM is also used in fixed wireless systems and wireless local-area network (WLAN) products. A system based on OFDM has been developed to deliver mobile broadband data service (WiMAX) at relatively high data rates.
OFDM systems are effectively a combination of modulation and multiple-access schemes that segments a communications channel in such a way that many users can share it. Whereas TDMA segments are divided according to time and CDMA segments are divided according to spreading codes, OFDM segments are divided according to frequency. It is a technique that divides the spectrum into a number of equally spaced tones (or frequencies) and carries a portion of a user's information on each tone. Although OFDM can be viewed as a form of frequency division multiplexing (FDM), it has the property that each tone is orthogonal to each other. FDM typically requires there to be frequency guard bands between the frequencies so that they do not interfere with each other. In contrast, OFDM permits the spectrum of each tone to overlap, but because they are orthogonal, they do not interfere with each other. By allowing the tones to overlap, the overall amount of spectrum required is reduced significantly
OFDM enables user data to be modulated onto the tones. The information is modulated onto a tone by adjusting the phase and/or amplitude of the tone. In the most basic form, a tone may be present or absent to indicate a single bit of information. Normally, however, either phase shift keying (PSK) or quadrature amplitude modulation (QAM) is typically employed. An OFDM system takes a data stream and splits it into N parallel data streams, each at a rate 1/N of the original rate. Each stream is then mapped to a tone at a unique frequency and combined together using the inverse fast Fourier transform (IFFT) to yield the time-domain waveform to be transmitted.
OFDM is a multiple-access technique since an individual tone or groups of tones can be assigned to different users. Multiple users share a given bandwidth, yielding an OFDMA system. Each user is assigned a predetermined number of tones when they have information to send. Alternatively, a user is assigned a variable number of tones based on the amount of information they need to send. The assignments are controlled by the media access control (MAC) layer, which schedules the resource assignments based on user demand.
OFDM can be combined with frequency hopping to create a spread spectrum system, realizing the benefits of frequency diversity and the interference averaging of CDMA. OFDM thus provides the best of the benefits of TDMA in that users are orthogonal to one another, and of CDMA, while avoiding the limitations of each, including the need for TDMA frequency planning and equalization, and multiple access interference in the case of CDMA.
The sinusoidal waveforms making up the tones in OFDM have the property of being the only Eigenfunctions of a linear channel. This property prevents adjacent tones in OFDM systems from interfering with one another. This property, and the incorporation of a small amount of guard time to each symbol, enables the orthogonality between tones to be preserved in the presence of multipath. This is what enables OFDM to avoid the multiple-access interference that is present in CDMA systems.
Considering the frequency domain representation of a number of tones, the peak of each tone corresponds to a zero level, or null, of every other tone. The result of this is that there is no interference between tones. When the receiver samples at the center frequency of each tone, only the energy of the desired signal is present, in addition to any noise that happens to be in the channel.
To maintain orthogonality between tones, it is necessary to ensure that the symbol time contains one or multiple cycles of each sinusoidal tone waveform. Normally this is the case since the system is constructed such that tone frequencies are integer multiples of the symbol period where the tone spacing is 1/T.
Note that in order to generate a pure sinusoidal tone, the signal must start at time minus infinity. This is important, because tones are the only waveform than can ensure orthogonality. The channel response, however, can be treated as finite, because multipath components decay over time and the channel is effectively band-limited. By adding a guard time, called a cyclic prefix, the channel can be made to behave as if the transmitted waveforms were from time minus infinity thus ensuring orthogonality, which essentially prevents one subcarrier from interfering with another, which is called intercarrier interference or ICI.
The cyclic prefix is a copy of the last portion of the data symbol appended to the front of the symbol during the guard interval. Multipath causes tones and delayed replicas of tones to arrive at the receiver with some delay spread. This leads to misalignment between sinusoids, which need to be aligned to be orthogonal. The cyclic prefix allows the tones to be realigned at the receiver, thus regaining orthogonality.
The cyclic prefix is sized appropriately to serve as a guard time to eliminate ISI. This is accomplished because the amount of time dispersion from the channel is smaller than the duration of the cyclic prefix. A fundamental trade-off is that the cyclic prefix must be long enough to account for the anticipated multipath delay spread experienced by the system. The amount of overhead increases, as the cyclic prefix gets longer. The sizing of the cyclic prefix forces a tradeoff between the amount of delay spread that is acceptable and the amount of Doppler shift that is acceptable.
An OFDM signal is the sum of N independent QAM symbols mapped onto N different subchannels with 1/T frequency separation where T is the OFDM symbol period. The discrete time-domain samples bi=(b0i,b1i, . . . , bN−1i) to be transmitted are obtained via an N-point inverse Fast Fourier Transform (IFFT) from the complex QAM symbols block ai=(a0i,a1i, . . . , aN−1i) as follows
                              b          n          i                =                              1                          N                                ⁢                                    ∑                              m                =                0                                            N                -                1                                      ⁢                                          a                m                i                            ⁢                              ⅇ                                  j2π                  ⁢                                                                          ⁢                                      mn                    /                    N                                                                                                          (        1        )            where ami is the QAM data symbol sent on the mth subcarrier of the ith OFDM symbol. A cyclic prefix is appended. Prior to passing through the PA, the OFDM signal undergoes D/A conversion and subsequently analog filtering and is mapped on a carrier frequency. For large N, the time domain samples bmi have a zero mean Gaussian distribution, as they are weighted sums of independent identically distributed random variables (the frequency domain QAM symbols ani. A small percentage of these time domain samples are thus susceptible to having high magnitudes at the tail of the distribution. These high magnitude samples cause the PAPR problem in OFDM. Mathematically, the PAPR of an OFDM block of digital samples b=(b0,b1, . . . ,bN−1) is defined as follows
                              PAPR          ⁡                      (            b            )                          =                                            max                              0                ≤                n                ≤                                  N                  -                  1                                                      ⁢                                                                            b                  n                                                            2                                            E            ⁢                                          {                                                                          b                                                        2                                }                            /              N                                                          (        2        )            where ∥•∥ denotes the Euclidean norm of the enclosed vector.
Today, there are both numerous wireless communication devices and wireless communication standard that make use of Orthogonal Frequency Division Multiplexing (OFDM) to carry high data rate traffic over a wireless channel. OFDM links are very robust to multipath fading conditions thus ensuring the required quality of service even under severe wireless channel conditions. Applications like Wireless LAN (WLAN), WiMAX and the upcoming 3G-LTE make wide use of OFDM as their transmission scheme.
As described supra, OFDM transmission uses a large number of subcarriers (often referred to as tones or bins), with orthogonal frequency separation between them, to carry the required information over the air. Modulation is often implemented using an IFFT while demodulation is performed using an FFT. The Wireless LAN (802.11.g) specification uses 52-56 subcarriers while the WiMAX make specification uses as many as 2048 subcarriers.
As the number of subcarriers increases, however, the probability of having higher voltage peaks as compared to the average power increases with a theoretical dependence ofPeak=log(Number of tones)  (3)The ratio between the maximum possible peak power to the average power is defined as the Peak to Average Power Ratio (PAPR). Another important aspect of the ratio between the peak power and average power of an OFDM transmission scheme is the amount of margin needed between the saturation point of the power amplifier (PA) to the average transmitted power of an OFDM scheme. The margin between the output saturation power of the PA to the average transmitted power at the PA output is referred to as backoff and is typically expressed in units of dB. A diagram illustrating the backoff for an example OFDM transmission signal is shown in FIG. 1. The backoff has a high correlation to the spectral mask and the error vector magnitude (EVM) at the output of the PA. Note that the EVM expresses the noise floor of the transmitter. As the backoff value increases, the spectral mask and EVM improve as well. An example spectral mask is shown in FIG. 2 wherein the frequency domain representation of the OFDM transmission signal 12 must meet the spectral mask constraint 10 as dictated by the relevant wireless standard.
OFDM transmitters often use different constellations depending on the available signal to noise ratio (SNR) at the receiver. This means that when the SNR at the receiver is low, the transmitter adjusts the constellation (i.e. often referred as ‘modulation format’) carried by all the OFDM subcarriers to be more robust, such as a simple scheme of BPSK often in combination with a strong error correcting code (ECC). When the SNR at the receiver is high, the transmitter uses a constellation of 64 QAM (often with lower ECC protection). This process is called ‘rate fallback’ in WLAN applications.
When the modulation format is simple (e.g., BPSK) the required EVM of the transmitter is likely high (e.g., −8 dB). Conversely, when the modulation format is complex, the required EVM of the transmitter is low (e.g., −25 dB). The spectral mask limitation of the transmitter, however, remains the same for all the modulation formats. This is why when the transmitter uses a simple modulation format such as BPSK it is limited by spectral mask constraints and not by the EVM, while for complicated modulation formats like 64 QAM, it is limited by the EVM. In WLAN applications with a typical PA, most transmitters use a backoff ratio of 8 dB for the QAM 64modulation format, while using a backoff of only 4 dB for BPSK modulation (since with BPSK, the transmitter is limited by spectral mask requirements and not by EVM requirements.
The high peak-to-average power ratio (PAPR) characterizing OFDM forces a reduction in the average power at the output of the power amplifier used in the transmitter. This is because the input signal to the PA must lie in the linear region of the PA, well below the saturation point. The increased linear dynamic range requirements typically translate to the need to use more costly PAs.
One way to avoid the extremely high backoff values and costly amplifiers of OFDM, occasional clipping and/or soft thresholding are allowed. This, however, leads to inband distortion that increases the bit error rate (BER) and causes spectral widening that increases adjacent channel interference.
Several OFDM PAPR reduction techniques have been suggested in the prior art, all of which attempt to reduce the required PA backoff and the effects of its nonlinearity. The various approaches are quite different from each other and impose different constraints.
In one prior art approach, several bits or bit sequences are used to carry a particular code that minimizes the PAPR of the resulting transmitted signal. The disadvantage, however, is that the data rate is reduced along with the PAPR. Other methods suggest using phase manipulations, such as selective mapping (SLM), partial transmit sequences (PTS) and random phasor. Although effective, these methods suffer from the disadvantages of high complexity and requiring coded side information to be transmitted. This causes problems in terms of compliance with wireless specifications.
Other methods such as tone reservation propose inserting anti-peak signals in unused or reserved subcarriers. Although the method does not cause any inband distortion, it does reduce the useful data rate. Although suited in some implementations (e.g., IEEE 802.16e), it is not always standards compliant (e.g., the bandwidth sacrifice required by this method is not permitted in IEEE 802.16d).
Other prior art approaches suggest altering the QAM constellation in order to reduce high signal peaks. The technique of tone injection relies on the principle of constellation expansion. It involves a complex optimization process, however, that makes it unattractive for systems with large numbers of subcarriers.
Additional prior art constellation extension methods have been suggested. Active constellation extension (ACE) allows the corner QAM constellation points to be moved within the quarter planes outside their nominal values. The other border points are allowed to be displaced along rays pointing towards the exterior of the constellation. The interior points are not modified, in order to preserve the minimum distance between the constellation symbols.
Further, a non-iterative PAPR reduction method relying on metric based symbol predistortion (MBSP) has been suggested. In this scheme, a predetermined number of corner constellation symbols are multiplied with a real valued constant greater than unity. A cost function then determines which symbols are to be modified. This algorithm is not recursive and it does not require the transmission of any side information. The number of symbols to be modified and the real-values expansion factor are predetermined by means of simulation.
It is thus desirable to have a mechanism that is capable of reducing or minimizing the backoff of an OFDM transmitter that does not suffer from the disadvantages of the prior art schemes described hereinabove. In addition, the reduced backoff mechanism should be flexible enough to enable reducing the required backoff while meeting any spectral mask and EVM constraints imposed by a wireless standard. Further, the reduced backoff mechanism preferably does not require changes to existing transmission formats or to the transmitter PHY hardware.